The least square straight line y = -2x + 3 to fit the data points (0, 3), (2, 1), (3, 1) is found. The minimum square error is 61.
Given data points are (0, 3), (2, 1), (3, 1).
To find the least square straight line, y = mx + b.
The line that fits these points will have the minimum square error.(0,3) y = mx + b; 3 = 0 + b; b = 3(2,1)
y = mx + b; 1 = 2m + b; b = 1 - 2m(3,1)
y = mx + b; 1 = 3m + b; b = 1 - 3m
Substitute the value of b in (2) and (3)1 - 2m = 3 - 3m; m = -2y = mx + b;
y = -2x + 3
The least square straight line y = -2x + 3 to fit the data points (0, 3), (2, 1), (3, 1) is found.
Now, we need to compute the minimum square error.
Square error of each point: Point 1 (0, 3): Square error = (3 - 3)² = 0
Point 2 (2, 1): Square error = (1 - (-4))² = 25
Point 3 (3, 1): Square error = (1 - (-5))² = 36
The minimum square error is the sum of the square error of all the points, Minimum square error = 0 + 25 + 36 = 61
Therefore, the least square straight line y = -2x + 3 to fit the data points (0, 3), (2, 1), (3, 1) is found. The minimum square error is 61.
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The graph of g(x) is a parabola that opens upward with a vertex at (-3, 4). Which statement is true?
A brewery produces a particular type of beer. If the process is running well then the probability that a randomly selected bottle is of good quality is 90%, independently of the quality of any of the other bottles. If the process is not running well then that probability is only 60%. Without further information, the probability that the process is running well is 80%. (a) 10 bottles are produced. Find the expected number of good quality bottles in this batch. (b) of this batch, the first 4 bottles are tested, and all are of good quality except for the second bottle. What is the probability that the process is running well? (c) The 5th bottle is now tested as well. What is the probability that this bottle is of good quality?
(a) The expected number of good quality bottles in this batch is 7.2
(b) The probability that the process is running well, given that the second bottle is not of good quality, is 0.5
(c) The probability that the 5th bottle is of good quality is 0.84
(a) To find the expected number of good quality bottles in the batch of 10 bottles, we can multiply the probability of each bottle being of good quality by the total number of bottles.
Given that the probability of a bottle being of good quality is 90% if the process is running well and 60% if the process is not running well, and the probability that the process is running well is 80%, we can calculate the expected number of good quality bottles as follows:
Expected number of good quality bottles = (Probability of running well) × (Probability of good quality | running well) × (Total number of bottles)
= (0.8) × (0.9) × (10)
= 7.2
Therefore, the expected number of good quality bottles in this batch is 7.2.
(b) Given that the first 4 bottles tested are all of good quality except for the second bottle, we need to find the probability that the process is running well.
Let A be the event that the process is running well, and B be the event that the second bottle is not of good quality.
Using Bayes' theorem, we can calculate the probability:
P(A | B) = (P(B | A) × P(A)) / P(B)
P(B | A) is the probability that the second bottle is not of good quality given that the process is running well, which is 1 - 0.9 = 0.1.
P(A) is the probability that the process is running well, which is given as 0.8.
P(B) is the probability that the second bottle is not of good quality. To calculate this, we need to consider the cases where the process is running well and not running well.
P(B) = P(B | A) × P(A) + P(B | not A) × P(not A)
= 0.1 × 0.8 + 0.4 × 0.2
= 0.08 + 0.08
= 0.16
Now, we can calculate the probability using Bayes' theorem:
P(A | B) = (0.1 × 0.8) / 0.16
= 0.5
Therefore, the probability that the process is running well, given that the second bottle is not of good quality, is 0.5.
(c) Now, if the 5th bottle is tested as well, we want to find the probability that this bottle is of good quality.
Let C be the event that the 5th bottle is of good quality.
Using the law of total probability, we can calculate the probability:
P(C) = P(C | A) × P(A) + P(C | not A) × P(not A)
= 0.9 × 0.8 + 0.6 × 0.2
= 0.72 + 0.12
= 0.84
Therefore, the probability that the 5th bottle is of good quality is 0.84.
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Which is the most reasonable estimate of 132% of 48?
a.5.2
b.6.5
c.52
d.65
The most reasonable estimate of 132% of 48 is 60. The correct answer is (C) 52.
To find the most reasonable estimate of 132% of 48,
A reasonable estimate does not exceed the original numbers in a problem. Let us look at a reasonable estimate.
we need to use the following formula:
Most reasonable estimate = Closest multiple of 10To use this formula, we first need to find 132% of 48.132% of 48 can be calculated as follows:132/100 x 48 = 63.36
Now, we need to find the closest multiple of 10 to 63.36.The closest multiple of 10 to 63.36 is 60.
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To find out the most reasonable estimate of 132% of 48, we can multiply the given percentage with 48.
Therefore, the most reasonable estimate of 132% of 48 is 64.
132% of 48 = (132/100) × 48
= 63.36
Since we are looking for an estimate, we can round off the above answer to the nearest whole number. Here, we have two possible options:
63 and 64.132% of 48 is slightly greater than half of 48 (which is 24) + 24. So, the answer should be slightly greater than 48 + 24 = 72. Therefore, the most reasonable estimate of 132% of 48 is 64. Thus, the correct answer is b.6.5.
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Draw a graph which has the following adjacency matrix: [2 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 (b) Label the vertices of your graph A, B, C, D (in any order). (c) How many different paths of length 10 are there from the vertex you labelled A to the vertex you labeled D in the graph you draw in part (a)?
Given an adjacency matrix, we need to find the graph which has the following adjacency matrix:[2 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0]We know that an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph.The diagonal elements of the matrix are always zero since self-loops are not allowed in a simple graph.The (i, j)-entry of the matrix is 1 if the ith vertex and jth vertex are adjacent, and 0 otherwise. Hence, for the given matrix, there is an edge between vertex 1 and vertex 2 and an edge between vertex 1 and vertex 3. Similarly, there are other edges between vertices.Here is the graph which has the given adjacency matrix:Graph with adjacency matrixFrom the graph above, we can label the vertices A, B, C, D in any order. Let's say we label the vertices as A = vertex 1, B = vertex 2, C = vertex 3, and D = vertex 4.Now, we need to find the number of different paths of length 10 from vertex A to vertex D.The number of paths of length n from vertex i to vertex j in a graph is given by the (i, j)-entry in the n-th power of the adjacency matrix. Here, we need to find the number of paths of length 10 from vertex 1 to vertex 4. So, we need to compute the 10th power of the given adjacency matrix:[2 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0] ^ 10We can use a calculator or software like MATLAB to compute the matrix power. After computing, we get that the (1, 4)-entry of the 10th power of the matrix is 8. Therefore, there are 8 different paths of length 10 from vertex A to vertex D.
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In circle O, radius OQ measures 9 inches and arc PQ measures 6π inches. Circle O is shown. Line segments P O and Q O are radii with length of 9 inches. Angle P O Q is theta. What is the measure, in radians, of central angle POQ? StartFraction 2 pi Over 3 EndFraction radians StartFraction 3 pi Over 4 EndFraction centimeters StartFraction 4 pi Over 3 EndFraction radians StartFraction 3 pi Over 2 EndFraction radians
The answer is A. 2pi/3 radians.
Answer:
First Option
Explanation:
A) 2pi/3 radians
Hope this helps :)
Write an equation in point-slope form and slope-intercept form for each line
1. passes through (1, 9), slope = 2
2. passes through (4, -1), slope = -3
An equation of a line in point-slope form: y - y₁ = m(x - x₁)
1.
passes through (1, 9) ⇒ x₁ = 1, y₁ = 9
slope: m = 2
The equation:
y - 9 = 2(x - 1) ← point-slope form
y - 9 = 2x - 2 {add 9 to both sides}
y = 2x + 7 ← slope-intercept form
2.
passes through (4, -1) ⇒ x₁ = 4, y₁ = -1
slope: m = -3
The equation:
y + 1 = -3(x - 4) ← point-slope form
y + 1 = -3x + 12 {subtract 1 from both sides}
y = -3x + 11 ← slope-intercept form
HELP NOW!!! 100 POINTS! Cylinder A has a radius of 10 inches and a height of 5 inches. Cylinder B has a volume of 750π. What is the percentage change in volume from cylinder A to cylinder B?
50% decrease
75% decrease
50% increase
200% increase
Answer:
50% increase
Step-by-step explanation:
The percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.
What is a cylinder?In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the formula for the volume of the cylinder is given by:
[tex]\rm V = \pi r^2h[/tex]
We have r = 10 inches and h = 5 inches
[tex]\rm V = \pi \times10^2\times5[/tex]
V = 500π cubic inches
Percent change in volume from cylinder A to cylinder B:
[tex]=\rm \frac{750\pi-500\pi}{500\pi} \times100[/tex]
= 50%
Thus, the percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.
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whats is the answer to this equation?
who ever gets the right answer gets 25 points.
Answer:
51.2 m
Step-by-step explanation:
To find perimeter add all sides up
The total number of passengers riding a certain city bus during the morning shift is 1,100. If the child's fare is $0.5o, the adult fare is $1.25, and the total revenue from the fares in the morning shift is $1,200, how many children and how many adults rode the bus during the morming shift? (Letx and y denote the number of children and adults, respectively.)
=1,000
=1,200
A total of 233 children and 867 adults rode the bus during the morning shift.
Let x represent the number of children and y represent the number of adults riding the bus during the morning shift.
We know that the total number of passengers is 1,100, so we can write the equation:
x + y = 1,100
The child's fare is $0.50, and the adult fare is $1.25. The total revenue from the fares is $1,200, so we can write another equation:
0.50x + 1.25y = 1,200
To solve this system of equations, we can use substitution or elimination.
Let's use substitution to solve for x:
From the first equation, we have: x = 1,100 - y
Substituting this into the second equation:
0.50(1,100 - y) + 1.25y = 1,200
Simplifying the equation:
550 - 0.50y + 1.25y = 1,200
0.75y = 650
y = 650 / 0.75
y ≈ 866.67
Since we can't have a fraction of a person, we can approximate y to the nearest whole number:
y = 867
Substituting this value of y back into the first equation:
x + 867 = 1,100
x ≈ 233
Therefore, approximately 233 children and 867 adults rode the bus during the morning shift.
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A recent study sought to determine if exercising after studying for an exam may help retain information. The 150 student volunteers that participated in the study were randomly assigned to three groups. All students were given a picture memory task that they studied for 15 minutes. After studying, one of the groups was instructed to exercise for 30 minutes immediately after studying. A second group was instructed to wait 1 hour after studying and then exercise for 30 minutes. The third group was instructed to not exercise after studying. The next day all 150 student volunteers were given a test to determine how well they could remember what they studied. Here are the results:
Answer:
The correct answer is (A).
Step-by-step explanation:
Because the data came from 3 groups in a randomized experiment, the appropriate test is a chi-square test for homogeneity.
Suppose the prevalence of is 12.5%. We assume the
diagnostic test has a sensitivity of 80% and a
95% specificity. What is the probability of getting a negative
result?
The probability of getting a negative result is 0.175 or 17.5%.
To calculate the probability of getting a negative result, we need to consider the sensitivity and specificity of the diagnostic test.
Given that the prevalence of the condition is 12.5%, we can assume that 12.5% of the population has the condition, and the remaining 87.5% does not.
The sensitivity of the test is 80%, which means that it correctly identifies 80% of the individuals with the condition as positive.
The specificity of the test is 95%, which means that it correctly identifies 95% of the individuals without the condition as negative.
To calculate the probability of getting a negative result, we need to consider both the true negative rate (1 - sensitivity) and the proportion of individuals without the condition (1 - prevalence).
Probability of getting a negative result = (1 - sensitivity) × (1 - prevalence)
= (1 - 0.80) × (1 - 0.125)
= 0.20 * 0.875
= 0.175
Therefore, the probability of getting a negative result is 0.175 or 17.5%.
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Can the following side measures make a triangle: 11in., 12in. and 13in?
Answer:
Yes
Step-by-step explanation:
Hello There!
Remember the sum of the two shorter sides has to be greater than the largest side in order for it to be a triangle
11+12 must be greater than 13
11+12=23
23>13 therefore the side lengths can form a triangle
HELP ASAP PLEASE ILL MARK BRAINLIEST
A backpack is on sale for 30% off. If the sales price is $15.75, what is the original price? Show your work.
Answer:
$22.50
Step-by-step explanation:
As it is 30% off, $15.75 is 70% of the full price. You can then divide 15.75 by 70 [= 0.225] to get 1% of the full price. Multiply 0.225 by 100 to get the full price. 0.225 x 100 = 22.5
We can check that this answer is correct by multiplying 22.50 by 0.7. If you get 15.75 you know the answer is correct as 15.75 is 70% of the full price.
If (81)(27)2x-5-93-4⁰, then x = ________
The value of x that satisfies the equation (81)(27)^(2x-5) - 9^(3-4x) = 0 is x = 17/14.
To find the value of x in the equation (81)(27)^(2x-5) - 9^(3-4x) = 0, we can use the properties of exponents and logarithms to simplify and solve the equation. By equating the bases and exponents on both sides, we can determine the value of x.
We start by simplifying the equation. Applying the exponent properties, we have (3^4)(3^3)^(2x-5) - (3^2)^(3-4x) = 0.
Simplifying further, we get (3^(4 + 3(2x-5))) - (3^(2(3-4x))) = 0.
Using the property (a^b)^c = a^(b*c), we can rewrite the equation as 3^(4 + 6x - 15) - 3^(6 - 8x) = 0.
Combining like terms, we have 3^(6x - 11) - 3^(6 - 8x) = 0.
To equate the bases and exponents, we set 6x - 11 = 6 - 8x.
Simplifying the equation, we get 14x = 17.
Dividing both sides by 14, we find that x = 17/14.
Therefore, the value of x that satisfies the equation (81)(27)^(2x-5) - 9^(3-4x) = 0 is x = 17/14.
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2/3 x 6 need help asap
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
2/3 x 6 is 4 because when you times the 2 in 2/3 u get 12 and 12/3 is the same as 4
Solving systems of equations using Substitution
Y= -4x +3
Y= 4x +3
A sample of 76 body temperatures has a mean of 98.7. Assume that o is known to be 0.5 °F. Use a 0.05 significance level to test the claim that the mean body temperature of the population is equal to 98.5 °F, as is commonly believed. What is the value of test statistic for this testing?
The value of the test statistic in the scenario given above is 3.487
The test statistic can be calculated as follows:
t = (mean - hypothesized mean) / (standard deviation / √(sample size))
mean = 98.7
hypothesized mean = 98.5
standard deviation = 0.5
sample size = 76
Plugging these values into the formula, we get the following test statistic:
t = (98.7 - 98.5) / (0.5 / √(76)) = 3.487
Therefore, the value of the test statistic in the above scenario is 3.487
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In a right triangle, one acute angle measure 35 degrees and its adjacent side is 40 yards.
Find the opposite side.
Paragraph. Describe how to find the opposite side of one right triangle with one acute angle of 35 degrees and adjacent side of 40 yards.
Word Bank: right triangle, opposite and adjacent side,
Answer:
Opposite side =28 yards
Step-by-step explanation:
Tan_°=Opposite÷ Adjacent
Tan 35° =Opposite÷40yards
Opposite=40*Tan35°
Opposite=28yards
3/4 + 7/8 + 5/6
(this is here because the question was too short)
Answer:23/8Step-by-step explanation:(LCM of 4,8 and 6 = 24 )
3×6/4×6 + 7×3/8×3 + 5×4/6×4 28+21+20/24
59/24
I hope you got it❤️❤️❤️And thanks your patience ❤️.SORRY
If cot θ= tan (pi/6) what is cos θ? Round your answer to the nearest hundredth.
Answer:3.46
Step-by-step explanation:
Can someone plz help me
Answer:
IT's d!!!!!
Step-by-step explanation:
What Is The Improper fraction for 6/7 and 4/5
Answer:
11 upon 4 is your 6 upon 4 answer
Help plssss I need to find mr pryor account balance
Answer:
$1,462.50
Step-by-step explanation:
We are to find the total amount after 4 years
Principal => $1,250
Rate => 4.25%
The formula to find the total amount =
A = P(1 + rt)
First, converting R percent to r a decimal
r = R/100 = 4.25%/100 = 0.0425 per year.
Solving our equation:
A = 1250(1 + (0.0425 × 4)) = 1462.5
A = $1,462.50
The total amount accrued, principal plus interest, from simple interest on a principal of $1,250.00 at a rate of 4.25% per year for 4 years is $1,462.50.
An airplane's altitude changed -378 feet over 77 minutes. What was the mean change of altitude in feet per minute?
Answer:
-4.91 feet
Step-by-step explanation:
Mean is a measure of central tendency. It is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = Total change in altitude / total time
378 / 77 = 4.91
when loaded with iron rods a lorry has mass of 12000kg. if the mass of iron rods is there times that of the empty lorry . find the mass or iron.
Complete Question
When loaded with iron rods a lorry has mass of 12000kg. if the mass of iron rods is three times that of the empty lorry, find the mass of iron.
Answer:
3000kg
Step-by-step explanation:
Let us represent
Mass of lorry = x
Mass of iron rods = y
x + y = 12000kg..... Equation 1
x = 12000kg - y
We are told that:
If the mass of iron rods is three times that of the empty lorry, find the mass of iron.
x = 3y
We substitute 3y for x in Equation 1
x = 12000kg - y
3y = 12000kg - y
Collect like terms
3y + y = 12000kg
4y = 12000kg
Divide both sides by 4
y = 12000kg/4
y = 3000kg
Note that:
Mass of iron rods = y
Hence, Mass of iron rods = 3000kg
Need to know if this is write. if not, please correct.
Classify each pair of angles listed below as adjacent or vertical.
I NEED HELP ASAPPPP ILL GIVE BRAINLIESTTTTTT
The number of peopie that have "liked" Mindy's Candy Store web
site can be represented by y = 270(1.65), where t is the number of weeks after a
review in a national magazine. Interpret the parameters of the equation. Make a
prediction about the future number of likes on the web site.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that, the number of people who liked Mindy's website is given by :
270(1.65)^t ; t = number of weeks after a review
Interpreting the equation :
The equation represents an exponential growth function :
y = a(1 + r)^t
a = initial amount ; r = growth rate ; t = period
Comparing the function with the equation given ;
270 = a = number of people who liked the website before the review
1 + r = 1.65
r = 1.65 - 1
r = 0.65 ; 0.65 * 100% = 65%
Site grew at a rate of 65% per week after review
Ther predicted number of likes 2 weeks after the review :
y = 270(1.65)^2
y = 270 * 2.7225
y = 735.075
Hence, number of likes after 2 weeks = 735
Lizzy had test scores of: 72, 94, 108, 60What is the RANGE of her test scores?
Answer:
48
Step-by-step explanation:
To find the range, you have to subtract the biggest/largest number by the smallest number:
108 - 60 = 48
The range is 48.